YES
  TPA v.1.0

Result: TRS is terminating

Default interpretations for symbols are not printed. For polynomial interpretations
and semantic labelling over N\{0,1} defaults are 2 for constants, identity for unary
symbols and x+y-2 for binary symbols. For semantic labelling over {0,1} (booleans)
defaults are 0 for constants, identity for unary symbols and disjunction for binary symbols.

[1]  TRS loaded from input file:
(1) app(app(F,app(app(F,f),x)),x) -> app(app(F,app(G,app(app(F,f),x))),app(f,x))

[2]  Label this TRS using following interpretation that is a model:
[app(x,y)] = x
[F] = 1
rest default

  thus obtaining new TRS:
(1a) app$11(app$11(F,app$11(app$11(F,f),x)),x) -> app$11(app$10(F,app$01(G,app$11(app$11(F,f),x))),app$11(f,x))
(1b) app$10(app$11(F,app$10(app$11(F,f),x)),x) -> app$11(app$10(F,app$01(G,app$10(app$11(F,f),x))),app$10(f,x))
(1c) app$11(app$11(F,app$11(app$10(F,f),x)),x) -> app$10(app$10(F,app$01(G,app$11(app$10(F,f),x))),app$01(f,x))
(1d) app$10(app$11(F,app$10(app$10(F,f),x)),x) -> app$10(app$10(F,app$01(G,app$10(app$10(F,f),x))),app$00(f,x))

[3]  Use following polynomial interpretation:
[app$11(x,y)] = x + 7y
rest default

  Remove rules with left hand side strictly bigger than right hand side:
(1a)-(1d)

[4]  Since there are no remaining rules, termination is proved!

../tpdb/TRS/higher-order/Kusakari/Ex6_11.trs, 0., Y
Couldn't open file <60>: 60: No such file or directory